If sin θ. Sin (2α+θ).sin(4α+θ)+...+sin(2nα+θ)= sin nθ/2^n-1 where 2nα=π, then cot θ+cot(2α+θ)+...+cot(2nα+θ)=

If f(x)=x²+x²/(1+x²)+x²/(1+x²)²+...+x²/(1+x²)ⁿ+... then x=0

d/dx{1-cos 2x/3+2 sin 2x}=

If x= a(cos θ+θ sin θ), y=a(sin θ-θ cos θ)then dy/dx=

If sec θ-cos θ, y= secⁿ θ- cosⁿ θ then (dy/dx)²=

d/dx{Tan^-1 1/√x²-1}=

If x= a(θ+sin θ), y=a(1-cosθ) then d²y/dx² at θ=π/4 is

d/dx{Tan^-1x/√1-x²+Sec^-11/√1-x²}=

d/dx{Tan^-1√(x²/a²-x²)}=

If y=sin(sin x)then y₂+(tan x)y₁+y(cos²x)=